Where is the Planck time?

Astronomy and Astrophysics – Astronomy

Scientific paper

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Scientific paper

It is widely believed that the Universe was created in a violent (kT ˜ h/tP ≈ 1029 eV) explosion lasting tP ≈ 5.4 x 10-44 s, where tP = (\hbar G/c5)(1)/(2), the Planck time, is an interval during which even time is a fuzzy concept. We present a method of directly testing whether time has its usual (i.e. classical) meaning on scales of <= tP. If indeed time and space cannot be known more precisely than tP and c tP, the same must apply to the period and wavelength of light, so that even the most monochromatic plane wave must in reality be a superposition of waves with independently varying ω and k, each having a different phase velcocity ω /k. For the entire accessible range of the electromagnetic spectrum this effect is extremely small, but can cumulatively lead to a complete loss of phase information if the emitted radiation propagated a sufficiently large distance. Since, at optical frequencies, the phase coherence of light from a distant point source is a necessary condition for the presence of diffraction patterns when the source is viewed through a telescope, such observations offer by far the most sensitive and uncontroversial test. We show that the HST detection of Airy rings from the active galaxy PKS1413+135, located at a distance of 1.2 Gpc, secures the exclusion of all first order Planck scale space-time fluctuations. This result may be used to deduce that the speed of light in vacuo is exact to a few parts in 1032.

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